{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization\n",
    "PySwarms implements tools for visualizing the behavior of your swarm. These are built on top of `matplotlib`, thus rendering charts that are easy to use and highly-customizable. However, it must be noted that in order to use the animation capability in PySwarms (and in `matplotlib` for that matter), at least one writer tool must be installed. Some available tools include:\n",
    "* ffmpeg\n",
    "* ImageMagick\n",
    "* MovieWriter (base)\n",
    "\n",
    "In the following demonstration, the `ffmpeg` tool is used. For Linux and Windows users, it can be installed via:\n",
    "```shell\n",
    "$ conda install -c conda-forge ffmpeg\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "# Change directory to access the pyswarms module\n",
    "sys.path.append('../')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on Python version: 3.6.3 |Anaconda custom (64-bit)| (default, Oct 13 2017, 12:02:49) \n",
      "[GCC 7.2.0]\n"
     ]
    }
   ],
   "source": [
    "print('Running on Python version: {}'.format(sys.version))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will demonstrate three plotting methods available on PySwarms:\n",
    "- `plot_cost_history`: for plotting the cost history of a swarm given a matrix\n",
    "- `plot_contour`: for plotting swarm trajectories of a 2D-swarm in two-dimensional space\n",
    "- `plot_surface`: for plotting swarm trajectories of a 2D-swarm in three-dimensional space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import modules\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "# Import PySwarms\n",
    "import pyswarms as ps\n",
    "from pyswarms.utils.functions import single_obj as fx\n",
    "from pyswarms.utils.plotters import (plot_cost_history, plot_contour, plot_surface)\n",
    "\n",
    "# Some more magic so that the notebook will reload external python modules;\n",
    "# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step is to create an optimizer. Here, we're going to use Global-best PSO to find the minima of a sphere function. As usual, we simply create an instance of its class `pyswarms.single.GlobalBestPSO` by passing the required parameters that we will use. Then, we'll call the `optimize()` method for 100 iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pyswarms.single.global_best:================================\n",
      "Optimization finished!\n",
      "Final cost: 0.0000\n",
      "Best value: [-0.00016964270606917298, -1.1965240885493259e-05]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "options = {'c1':0.5, 'c2':0.3, 'w':0.9}\n",
    "optimizer = ps.single.GlobalBestPSO(n_particles=50, dimensions=2, options=options)\n",
    "cost, pos = optimizer.optimize(fx.sphere_func, iters=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the cost history\n",
    "\n",
    "To plot the cost history, we simply obtain the `cost_history` from the `optimizer` class and pass it to the `cost_history` function. Furthermore, this method also accepts a keyword argument `**kwargs` similar to `matplotlib`. This enables us to further customize various artists and elements in the plot. In addition, we can obtain the following histories from the same class:\n",
    "- mean_neighbor_history: average local best history of all neighbors throughout optimization\n",
    "- mean_pbest_history: average personal best of the particles throughout optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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wTxHxuswcLfZ7Z2Y+2a3ay8DBBkmS1E43O3ELgNWZ+WBmvgTcCCxsWLMQuL64fQtwckRE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\nenUOMBdYWlwvdx2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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcb041c0400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cost_history(cost_history=optimizer.cost_history)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Animating swarms\n",
    "The `plotters` module offers two methods to perform animation, `plot_contour()` and `plot_surface()`. As its name suggests, these methods plot the particles in a 2-D or 3-D space.\n",
    "\n",
    "Each animation method returns a `matplotlib.animation.Animation` class that still needs to be animated by a `Writer` class (thus necessitating the installation of a writer module). For the proceeding examples, we will convert the animations into an HTML5 video. In such case, we need to invoke some extra methods to do just that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# equivalent to rcParams['animation.html'] = 'html5'\n",
    "# See http://louistiao.me/posts/notebooks/save-matplotlib-animations-as-gifs/\n",
    "rc('animation', html='html5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, it would be nice to add meshes in our swarm to plot the sphere function. This enables us to visually recognize where the particles are with respect to our objective function. We can accomplish that using the `Mesher` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyswarms.utils.plotters.formatters import Mesher"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize mesher with sphere function\n",
    "m = Mesher(func=fx.sphere_func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are different formatters available in the `pyswarms.utils.plotters.formatters` module to customize your plots and visualizations. Aside from `Mesher`, there is a `Designer` class for customizing font sizes, figure sizes, etc. and an `Animator` class to set delays and repeats during animation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting in 2-D space\n",
    "\n",
    "We can obtain the swarm's position history using the `pos_history` attribute from the `optimizer` instance. To plot a 2D-contour, simply pass this together with the `Mesher` to the `plot_contour()` function. In addition, we can also mark the global minima of the sphere function, `(0,0)`, to visualize the swarm's \"target\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make animation\n",
    "animation = plot_contour(pos_history=optimizer.pos_history,\n",
    "                         mesher=m,\n",
    "                         mark=(0,0))\n",
    "\n",
    "# Enables us to view it in a Jupyter notebook\n",
    "HTML(animation.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save as GIF\n",
    "animation.save('plot_contour.gif', writer='imagemagick', dpi=96)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting in 3-D space\n",
    "\n",
    "To plot in 3D space, we need a position-fitness matrix with shape `(iterations, n_particles, 3)`. The first two columns indicate the x-y position of the particles, while the third column is the fitness of that given position. You need to set this up on your own, but we have provided a helper function  to compute this automatically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Obtain a position-fitness matrix using the Mesher.compute_history_3d()\n",
    "# method. It requires a cost history obtainable from the optimizer class\n",
    "pos_history_3d = m.compute_history_3d(optimizer.pos_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make a designer and set the x,y,z limits to (-1,1), (-1,1) and (-0.1,1) respectively\n",
    "from pyswarms.utils.plotters.formatters import Designer\n",
    "d = Designer(limits=[(-1,1), (-1,1), (-0.1,1)], label=['x-axis', 'y-axis', 'z-axis'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make animation\n",
    "animation3d = plot_surface(pos_history=pos_history_3d, # Use the cost_history we computed\n",
    "                           mesher=m, designer=d,       # Customizations\n",
    "                           mark=(0,0,0))               # Mark minima\n",
    "\n",
    "# Enables us to view it in a Jupyter notebook\n",
    "HTML(animation3d.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save as GIF\n",
    "animation3d.save('plot_surface.gif', writer='imagemagick', dpi=96)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
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 "nbformat_minor": 2
}
